Physics A2 Final UP TO DATE

(Equation) Give the equation for Specific Latent Heat Give the Units What is L sometimes written out as?

E = mL or energy change = mass of substance changed x specific latent heat Units of L: J kg⁻¹ L is usually written as Lv for latent heat of vaporization and Lf for latent heat of fusion.

Describe the kinetic model of a Gas (see page 4 for diagrams)

Particles are free to move around with constant random motion. There are no forces of attraction between particles in an ideal gas

Describe the kinetic model of a Solid (see page 4 for diagrams)

Particles vibrate about fixed positions in regular lattice. They're held in position by strong forces of attraction

What do physicists picture in kinetic theory?

Picture gas particles moving at high speed in random directions

(Equation +) Describe and explain Charles's Law

Says that at a constant pressure, the volume, V of a gas is directly proportional to its absolute temperature, T Equation: V/T = Constant or Volume/Temperature = Constant

Make sure you are happy with the calculation on page 27 with Kepler's 3rd Law Calculations (and clever Ratio's)

See Book

Make sure you are fine with finding the specific heat capacity of a material.

See page 6

What is special about the energy molecules in a gas have?

Some don't have much kinetic energy and move slowly. Others have loads of kinetic energy and whizz along. But most however are somewhere in between

Make your you are happy with the graph and calculation example on page 24 for gravitational potential

Sure

Define: Specific Heat Capcity

The Specific heat capacity (c) of a substance is the amount of energy needed to raise the temperature of 1 kg of the substance by 1 K (or 1°C).

What does the specific heat capacity effect?

When you heat something, the amount of energy needed to raise its temperature depends on its specific heat capacity.

What is special about zero kelvin?

Zero kelvin is the lowest possible temperature and is called absolute zero.

(Equation +) Describe and explain Boyle's law, giving the equation. (See graph on page 8)

1 At a constant temperature, the pressure p and volume V of a gas are inversely proportional. 2. (The higher the temperature of the gas, the further the curve is from the origin) Equation: pV = Constant or Pressure x Volume = Constant

What are the 2 key numeric points for converting between Celsius and Kelvin?

1. A change in 1 K = a change in 1°C 2. To change from Celsius into Kelvins you simply add 273

What does a Maxwell-Boltzmann graph show?

1. A graph of the numbers of molecules in a gas with different kinetic energies 2. It is a theoretical model which has been developed to explain scientific observations.

How would you conduct an experiment and find the specific heat capacity of the material? (2/2)

1. Heat the substance with the heater. You need a temperature rise of about 10 K to get an accurate value of C. 2. With an ammeter and voltmeter attached to your electric heater you can work out the energy supplied 3. Plug data into E = mcΔθ to calculate c (Alternatively you can plot a graph - practical book for more detail).

How would you setup an experiment to measure the Specific Heat Capacity of a solid? What about with a liquid? (1/2)

(See Diagram on page 6) 1. Use electric heater, digital thermometer, insulating material and a solid. 2. Similar setup but with a heating coil instead of a electric heater if you wish, and an insulating lid on top.

Explain how Mases in a Gravitational Field experience a Force of Attraction

1. A gravitational field is a force field - a region where an object will experience a non-contact force. 2. Force fields cause interactions between objects or particles - e.g. static or moving charges interact through electric fields and objects with mass interact through gravitational field. 3. Any objects with mass will experience an attractive force if you put in the gravitational field of another object. 4. Only objects with a large mass, such as stars and planet have a significant effect. E.g. the gravitational fields of the Moon and the Sun are noticeable here on earth - they're the main cause of our tides.

State Kepler's Second Law See diagram on page 27

1. A line joining the Sun to a planet will sweep out equal areas in equal times 2. (So if moving from A to B takes the same amount of time as going from C to D, the two shared sections will have equal areas.

What are satellites?

1. A satellite is just any smaller mass which orbits a much larger mass - the Moon is a satellite of the Earth 2. In our Solar System, the planets have nearly circular orbits, so you can use equations of circular motion

Explain what Internal energy is

1. All things (solids, liquids, gases) have energy contained within them. 2. The amount of energy contained in a system is called its internal energy - it is found by summing the kinetic and potential energies of all the particles within it.

Explain how Newton's Law of Gravitation can be used to investigate the thickness of a planet's atmosphere

1. As well as predicting the motion of satellites, Newton's law of gravitation can also help to explain how thick a planet's atmosphere is 2. The planet's gravitational field exerts a force on everything around it, including the particles which make up its atmosphere .Otherwise,the particles would float off into space. 3. The more massive the planet is, the larger the force is further away from the planet's surface - so the more atmosphere particles it can stop escaping into space, leading to a thicker atmosphere.

Derive the formula for Escape Velcotiy

1. As you know energy (kinetic energy + gravitational potential energy) is zero: 1/2mv² + (-GMm/r) = 0 so 1/2mv² = GMmr 2. Canceling the m's gives: 1/2v² = GM/r (this shows the escape velocity is the same for all masses in the same gravitational field 3. Rearrange for velocity, v: v² = 2GM/r → v = √(2GM/r)

Briefly state the 3 gas laws

1. Boyle's Law: pV = Constant 2. The Pressure Law: P/T = Constant 3. Charles's Law: V/T = Constant

Who provided explanations for Brownian Motion and what did they discover?

1. Brown couldn't explain this 2. Einstein showed up 10 years late and showed this proved evidence for the existence of atoms or molecules in the air (the kinetic model of matter). 3. The randomly moving air particles were hitting the smoke particles unevenly, causing this motion.

(Equation +) Derive and explain the Equation of State Explain what each symbol is and give units

1. Combining all the gas laws gives the equation p(v/T) = Constant 2. The constant then becomes nR, where R is called the molar gas constant. ts value is 8.31 Jmol⁻¹K⁻¹. Plugging this in gives the following equation: P(V/T) = nR or rearranged pV = nRT <== The equation of state of an ideal gas p is Pressure (Pa), V is volume (m³), T is temperature (K), n is amount of gas in moles

(Equation + ) Derive the Equation relating speed, mass and radius of a satellite.

1. Earth feels a force due to the gravitational 'pull' of the Sun. The force is given by Newton's law of gravitation: (F = -(GMm)/r² 2. The earth has velocity v. Its linear speed is constant but its direction is not - so it's accelerating . The centripetal force (p.14) causing the acceleration is: F = mv²/r 3. The centripetal force on the Earth must be a result of the gravitational force due to the Sun, and so these forces must be equal: (mv²)/r = (GMm)/r² which results in : * v = √(GM/r) *

Explain the elements of the formula: g = F/m

1. F is the force experienced by a mass m when it's placed in the gravitational field . Divide F by m and you get the force per unit mass. 2. g is a vector quantity, always pointing towards the centre of the mass whose field you're describing. Depending on the direction defined to be positive, it could be negative 3. Since the gravitational field is almost uniform at the Earth's surface, you can assume g is a constant if you don't go too high. 4. g is just the acceleration of a mass in gravitational field - often called the acceleration due to gravity.

What is special about the graph of Temperature v. Pressure when it comes to the pressure law?

1. For any ideal gas, the line meets the temperature axis at -273°C - that is absolute zero 2. If the graph is in kelvins, it would go through the origin.

What is an ideal gas? How do real gases behave in comparison?

1. Gases that obey all the assumptions of the kinetic model are called ideal gases. 2. Real gases behave like ideal gases as long as the pressure isn't too big and the temperature is reasonably high (compared to their boiling points).

Explain what Geostationary Satellites are.

1. Geostationary satellites orbit directly over the equator and are always above the same point on Earth 2. A geostationary satellite travels at the same angular speed as the earth turns below it 3. Their orbit takes exactly one day

Explain why the gravitational potential is negative and what the formula V(g) = -GM/r shows

1. Gravitational potential is negative - you have to do work against the gravitational field to move an object out of it. 2. The further you are from the centre of a radial field, the smaller the magnitude of V(g).. 3. At an infinite distance from the mass, the gravitational potential will be 0.

How would you estimate the Specific Heat Capacity of a Metal Block using the Method of Mixtures? (Some b's, s's and w's are subscript. See page 6 for clarification)

1. Heat a block of known mass mw up to a temperature Tb 2. Quickly transfer this block into a container containing a mass of water, mw, at a temperature Tw. 3. The hot block will heat the water. Measure the temperature of water once it has reached a steady value, Ts. 4. The heat (energy) gained by the water is equal to the heat lost by the block so: mwcwΔθw = mbcbΔθb which becomes mwcw(Ts-Tw) = mbcb(Tb-Ts) 5. Rearrange for Cb this makes: cb = (mwcw(Ts-Tw))/(mbcb(Tb-Ts))

Explain what to do in gas law experiments if markings are quite far apart

1. If the markings on your measuring equipment are quite far apart you can usually interpolate between them . 2. (e..g. if the temperature is halfway between the markings for 24°C and 25°C you could record it as 24.5°C 3. However it's better to use something with a finer scale if you can

(Equation +) Derive and explain an equation relating pressure, volume, Number of Particles, Boltzmann constant, and temperature.

1. If you combine N = n x NA and k = R/NA, you'll see that Nk = nR. 2. This can be substituted into the equation of state to give this alternative form (in terms of the number of particles N, rather than the moles, n) pV = nkT p = Pressure (Pa) V = volume (m³) T = temperature (K) N = number of particles k = Boltzmann constant (1.30x10⁻²³)

Explain the gravitational field lines of the earth in relation to a small mass m (See diagram on page 22)

1. If you put a small mass, m, anywhere in the Earth's gravitational field, it will always be attracted towards the earth 2. The Earth's gravitational field is radial - the lines of force meet at the centre of the Earth. 3. If you move mass m further away from the Earth - where the lines of force are further apart - the force it experiences decreases. 4. The small mass, m, has a gravitational field of its own. This doesn't have a noticeable effect on the Earth though because the Earth is so much more massive. 5. Close to the Earth's surface, the field is (almost) uniform - the field lines are (almost) parallel and equally spaced. You can usually assume that the field is perfectly uniform.

Describe and explain an experiment to estimate absolute zero (Pressure Law) (See Page 8 for diagram)

1. Imerese a stoppered flask of air in a beaker of water so that as much as possible of the flask is submerged. Connect the stopper to a Bourdon gauge using a short length of tube - the volume of the tubing must be much smaller than the volume of the flask. Record the temperature of the water and the pressure on the gauge. 2. Heat the water for a few minutes then remove the heat, stir the water to ensure it is at a uniform temperature and allow some time for the heat to be transferred from the water to the air. Record the pressure on the gauge and the temperature, then heat the water again and repeat until the water boils. 3. Repeat your experiment twice more with fresh cool water 4. Plot you results on a graph of pressure against temperature (in °C). Draw a line of best fit. Estimate the value of absolute zero by continuing (extrapolating) your line of best fit until it crosses the x axis (should hit -273°C).

Explain the idea of Brownian Motion

1. In 1827, botanist Robert Brown noticed that tiny particles of pollen suspended in water moved with a a zigzag, random motion. 2. This type of movement is known as Brownian motion

Explain how the following are conserved: 1. Number of quarks (excluding beta decay). 2. Charge (Make sure you are happy with !'s on page 69)

1. In all other kinds of interactions (excluding beta plus and minus), the number of quarks of any time must be the same before and after the interaction 2. In ALL interactions, charge must be conserved - the total charge before = the total charge after.

In terms of quarks, explain what happens in terms of quarks for beta-minus (β⁻) decay. (See diagram on Page 69)

1. In beta-minus (β⁻) decay, a neutron is changed into a proton - in other words udd changes into uud. It means turning a d quark into a u quark. 2. In terms of quarks: d → u + e⁻ + ν (with line over the top) 3. In terms of Charge: (-1/3) → (+2/3) + (-1) + 0

Explain what the Root Mean Squared Speed is (or crms) (rms subscript)

1. It often helps to think about the motion of a typical particle in kinetic theory 2. c(bar)² is the mean square speed and has units m²s⁻² 3. c(bar)² is the average of the squared speeds of all the particles, so the square root of it gives you the typical speed. 4. This is called the root mean square speed, or usually the r.m.s speed. It is often written as crms. The unit is the same as any speed - ms⁻¹ 5. Crms can be found by square rooting the mean square speed √(c²)

(Extra?) Explain the origin of Kepler's Laws

1. Kepler came up with three laws about 1600, about 80 years before Newton developed his law of gravitation. 2. They're usually used to describe the planets in our solar system, but they can be used for any object and its satellite.

Explain moles and Avogadro's Constant, and give it's value.

1. One mole of any material contains the same number of particles, no matter what the material is. 2. This number is called Avogadro's Constant and has the symbol NA (A is subscript) 3. The value of NA is 6.02x10²³ particles per mole

(Equation +) State and explain the formula relating the gravitational field strength with radius, Mass and the Gravitational constant See graph on page 23

1. Point masses have radial gravitational fields (see other cards). 2. The value of g depends on the distance r from the point mass M. This gives: g = -GM/r² It is another example of an inverse square law - as r increases, g decreases.

In terms of quarks, explain what happens in terms of quarks for beta-plus (β⁺) decay. (See diagram on Page 69)

1. Some unstable isotopes like carbon-11 decay by beta-plus (β⁺) emission. - In this case a proton changes to a neutron, so a u quak changes to a d quark. 2. In terms of quarks: u → d + e⁺ + ν 3. In terms of Charge: (+2/3) → (-1/3) + (+1) + 0

Explain the Zeorth Law of Thermodynamics

1. Suppose A, B and C are three identical metal blocks (see page 5 for diagram). A has been in a warm oven, B has come from a refrigerator and C is at room temperature. 2. Thermal energy flows from A to C and C to B until they all reach thermal equilibrium and the net flow of energy stops, This happens when the three blocks are at the same temperature.

(Equation +) State and explain relating Boltzmann constant, the molar gas constant and Avogadro's constant State the value of Boltzmann constant

1. The Boltzmann constant, k, is given by k = R/NA 2. You can think of the Boltzmann constant as the gas constant for one particle of gas, while R is the gas constant for one mole of gas. 3. The value of Boltzmann constant is 1.30x10⁻²³ JK⁻¹

Explain the uses and similarities and differences between the Celsius and Kelvin (thermodynamic) scales. Don't reference numeric values

1. The Celsius scale uses the freezing and boiling points of water (0°C and 100°C) to make a temperature scale which can be easily used on a day to day basis. 2. However, scientists use the kelvin scale (the absolute scale of temperature) for all equations in thermal physics 3. It is also known as the thermodynamic scale, and it does not depend on the properties of any particular substance, unlike the celsius scale.

Give some key points about Maxwell-Boltzmann graphs (as shown on page 12)

1. The curve starts at (0,0) as no molecules have zero energy 2. Most molecules are moving at a moderate speed so their energies are within the main section 3. Relatively few molecules are moving slowly (they are in the bottom left section). 4. Relatively few molecules are moving quickly (they are in the bottom right section)

Define/Explain what escape velocity is

1. The escape velocity is defined as the velocity needed so an object has just enough kinetic energy to escape a gravitational field. 2. This is when an object's kinetic energy is equal and opposite to its gravitational potential energy - so the total energy is 0.

When doing an experiment to find the specific heat capacity of a material, what is important to note about the final value? What can be done to solve this?

1. The final value for C will be a large overestimate. (Note that this is not always the case in all experiments (e.g. starting at a low temperature. etc. ). 2. This is because some of the energy from the heater gets transferred to the air and the container. 3. This source of error can be decreased by starting below and finishing above room temperature to cancel out gains and losses. 4. Temperature will continue to rise when turned off - so if using the non graph method, it is important to continue noting temperature rise until it begins to fall again once the heater is switched off.

Explain the forces experienced on an 2 objects in a gravitational field

1. The force experienced by an object in a gravitational field is always attractive. It's a vector which depends on the masses involved and the distance between them. 2. The diagram on page 22 shows the force acting on mass m due to mass M. (The force on M due to m is equal and in the opposite direction 3. M an m are uniform spheres which behave as point masses (as it all mass is concentrated at the centre.

Give the assumptions in the kinetic model

1. The gas contains a large number of particles. 2. The particles move rapidly and randomly. 3. The volume of the particles is negligible when compared to the volume of the gas. 4. Collisions between particles themselves or between particles and the walls of the container are perfectly elastic. 5. The duration of each collision is negligible when compared to the time between collisions 6. There are no forces between particles except for the moment when they are in collision.

Explain the graph of Force v. Distance on page 24

1. The graph shows how the force on an object, due to gravitational field of a point mass, varies with the object's distance, r, from the point mass. 2. The area under the curve between the two values of r gives the work done to move the object from one point to the other

Explain what gravitational potential is (g) are subscript)

1. The gravitational potential V(g), at a point is the work g in moving a unit mass from infinity to that point

Describe and explain what can be used to describe matter Why was this not accepted at first?

1. The idea that solids, liquids and gases are made up of tiny moving or vibrating particles is called the kinetic model of matter. 2. It seems obvious now, but this wasn't always accepted by the scientific community. It took several scientists and hundreds of years to develop a controversial idea into an accepted theory

State and explain the various energies that makeup Internal Energy

1. The kinetic energy of a particle depends on its mass and speed. Through kinetic theory, the average kinetic energy is proportional to temperature - the hotter the temperature, the higher the average kinetic energy 2. Potential energy is caused by interactions between particles and is based on their positions relative to each other These energies are randomly distributed amongst the particles

(Equation) State and explain the equation that links number of particles, number of moles and Avogadro's constant

1. The number of particles, N, in an amount of gas is given by the number of moles, n, multiplied by Avogadro's constant, NA (6.02x10²³) 2. Equation: N = n x NA

(Equation +) Derive the equation relating Time Period, Mass and radius of a satellite.

1. The time taken for one orbit is called the period, T (in seconds). For circular motion T = (2πr)/v . 2. Substituting this into v = √(GM/r) and rearranging gives: * T² = (4π²/GM)r³

Explain the latent heat of fusion

1. To melt a solid, you need to break the bonds that hold the particles in place. 2. The energy needed for this is called the latent heat of fusion

Explain what Gravitational potential difference is

1. Two points at different distances from a mass will have different gravitational potentials (because the magnitude of the gravitational potential decreases with distance) - this means that there is a gravitational potential difference between those two points. 2.When you move an object you do work against gravity - the amount of energy you need depends on the mass of the object and the gravitational potential difference you move it through.

Explain the latent heat of vaporaisation

1. When you boil or evaporate a liquid, energy is needed to pull the particles apart completely. 2. This is the latent heat of vaporisation

Explain what happens to energy during a change in phase. Give an example

1. When you heat a substance, you increase its temperature - thereby increasing the kinetic energy of the particles within it and its internal energy. 2. When a substance changes phase, its internal energy changes, but its kinetic energy (and temperature) doesn't. This is because the change of phase is altering the bonds and therefore potential energy of the particles. 3. For example, in a pan of boiling water, the potential energy of the water molecules increases as they break free of the liquid. But the water in both places is at 100°C

Describe and explain an experiment that you can do to investigate pressure and volume (Boyle's Law) (See Page 8 for diagram)

1. You can investigate the effect of pressure on volume by setting up the experiment shown on page 8. The oil confines a parcel of air in a sealed tube with fixed dimensions. A tyre pump is used to increase the pressure in the tube and the Bourdon gauge records the pressure. As the pressure increases the air will compress and the volume occupied by the tube will reduce 2. Measure the volume of air when the system is at atmospheric pressure, then gradually increase the pressure noting down both the pressure and the volume of air Multiplying them together at any point should give a constant.

What are the advantages and disadvantages of satellites?

ADV: 1. These satellites are really useful for sending TV and telephone signals and have improved communication around the world. 2. The satellite is stationary relative to a certain point on the Earth so you don't have to alter the angle of your receiver (or transmitter) to keep up. DIS: 1. Expensive 2. Pose a small risk of something going wrong and the satellite falling back to earth

Explain the energy at zero Kelvin

At 0 K all particles have the minimum possible internal energy - everything theoretically stops - at higher temperatures, particles have more energy. (In fact with the Kelvin Scale, a particles energy is proportional to temperature (see later cards/page 13)).

(Equation +) Describe and explain the Pressure law, giving the equation. (See graph on page 8)

At a constant volume the pressure, p of a gas is directly proportional to its absolute temperature T Equation: p/T = Constant or Pressure/Time = Constant

Ensure you are happy with orbital calculations on (page 26)

Coool

(Equation) Give the equation for Specific Heat Capacity What are the units? How is the formula sometimes subtly different?

E = mcΔθ or Energy change = mass x specific heat capacity x change in temperature Units: Jkg⁻¹K⁻¹ or Jkg⁻¹°C⁻¹ Q is sometimes used instead of E for the change in thermal energy

State Kepler's First Law See diagram on page 27

Each planet moves in an ellipse around the Sun, with the Sun at one focus (a circle is just a special kind of ellipse).

What can particles mean in a gas?

Either molecules or atoms

(Equation) Give Newton's Law of Gravitation Explain the origin of the negative sign

F = -(GMm)/r² or Force (acting on mass m due to M) = (the gravitational constant - 6.67x10⁻¹¹ Nm²kg⁻² x Mass 1 x mass 2)/(RadiusSquared) The negative sign shows that vector F is in the opposite direction to r (displacement of m from M)

Be sure you are familiar with the Maxwell-Boltzmann graph on page 12 CGP

Fab

How can Brownian Motion be observed in the Lab?

Follow this method: 1. Put some smoke in a brightly illuminated glass jar and observe the particles using a microscope. 2. The smoke particles appear as bright specks moving haphazardly from side to side, and up and down.

Explain how you can measure the specific latent heat of a solid or a liquid

For a solid: 1. Put a heating coil and equal masses of ice into two funnels above beakers 2. Turn on one heating coil for three minutes. Record the energy transferred in the three minutes. Dont turn on the other coil - use it to measure how much ice melts due to the ambient temperature of the room 3. After 3 minutes, measure the mass of water collected in the beakers. Subtract one from the other to get the mass of ice, m, that melted solely due to the presence of the heater 4. E = ml, so to find the specific latent heat of fusion for water just divide the energy supplied by the mass of ice that melted: L = E/m For a liquid: very similar experiment but boil the water in a distilling flask, condense the vapour given off and divide the energy transferred by the mass of condensed water collected.

What are gravitational field lines?

Gravitational field lines (or lines or force) are arrows showing the direction of the force that masses would feel in a gravitational field.

(Equation (Learn) +) What is gravitational field strength? Give an equation to show it, units and the value on earth

Gravitational field strength, g, is the force per unit mass. Its value depends on where you are in the field. It can be calculated by the following formula: g = F/m where g is in newtons per kilogram (Nkg⁻¹) The value of g at the Earth's surface is approx 9.81 Nkg⁻¹ or ms

(Equation + ) Explain and derive the formula showing how an object's gravitational potential energy depends on its mass.

Gravitational potential is work done per unit mass, so the gravitational potential energy (E) of an object in a gravitational field is: E = mVg. Subbing in the formula for Vg, the gravitational potential energy of an object of mass m is: E = m(-GM/r) = -GMm/r where E is gravitational potential energy (J) and r is the distance form the centre of M to the centre of m (m)

Define: Zeroth Law of Thermodyanamics

If body A and body B are both in thermal equilibrium with body C, then body A and body B must be in thermal equilibrium with each other.

Describe the kinetic model of a Liquid (see page 4 for diagrams)

Particles are constantly moving around and are free to move past one another but are attracted to each other

Use Newton's Laws to Explain the Pressure of an Ideal Gas

Imagine a cubic box containing N particles of an ideal gas each with a mass m 1. The particles of the gas are free to move around with constant, random motion. There are no forces of attraction between the particles, so according to Newton's 1st they continue to move with constant velocity until they collide with another particle or the box itself. 2. When a particle collides with a wall of the box, it exerts a force on the wall, and the wall exerts an equal and opposite force back (This is Newton's 3rd) 3. The size of the force exerted on the particle on the wall can be calculated using Newton's 2nd Law, which says that the force is equal to the rate of change of momentum. 4. For example, if particle Q is travelling directly towards wall A with velocity u, its momentum is mu. When it hits the wall, the force of the impact causes it to rebound in the opposite direction at the same speed. It's momentum is now -mu , which means the change in momentum is 2mu. 3. So, the force of a particle exerts is proportional to its mass and its velocity. The mass of a single gas particle is tiny (1 atom of helium is 6.6x10⁻²⁷ kg). So each particle can only exert a miniscule force. 6. But there are around millions of billions of particles in a box. The combined force is much bigger than the contribution from any individual particle. 7. Because there are so many particles in the box, a significant number will be colliding with each wall of the box at any given momentum, And because the particle's motion is random, the collisions will be spread all over he surface of each wall. The result is a steady, even force n all of the walls of the box - this is pressure.

(Equation +) State and explain the equation for gravitational potential including units

In a radial field (like the Earth's), the equation for gravitational potential is: V(g) = - GM/r Where V(g) is gravitational potential (Jkg⁻¹), G is the gravitational constant, M is the mass of the object causing the gravitational field (kg), and r is the distance from the centre of the object (m).

Explain the effect of changing the volume with the equation pV = 1/3Nmc².

Increasing the volume of the container decreases the frequency of collisions because particles have further to travel in between collisions. This decreases the pressure

Define: Internal Energy

Internal energy is the sum of kinetic energy and potential energy of the particles within a system. (It is 0J as a gas, a large negative number when in a liquid and an even larger negative number when a solid)

What conditions are needed for the Equation of State to give an accurate answer?

It works well (i.e., real gases approximate to an ideal gas) for gases at low pressures and fairly high temperatures.

(Really?) What is Kelvin named after?

Lord Kelvin who first suggested it

Make sure you are happy with escape velocity calculations such as that on page 25

Ok

Explain speed with the equation pV = 1/3Nmc².

The faster the particles are going when they hit the walls, the greater the change in momentum and force exerted.

What is special about the energy required, the time taken to change state and the mass?

The larger the mass of the substance, the more energy it takes to change its state.

Explain, giving a formula, how Newton's Law of Gravitation is an Inverse Square Law

The law of gravitation is an inverse square law so: F ∝ 1/r² 1. If the distance r between the masses increases then the force F will decrease 2. If the distance doubles then the force will be one quarter the strength of the original force

Explain mass with the equation pV = 1/3Nmc².

The mass, m, of the particles - according to Newtons 2nd Law, force is proportional to mass, so heavier particles will exert a greater force.

Explain the effect of changing the number of particles with the equation pV = 1/3Nmc².

The number of particles, N, - increasing the number of particles increases the frequency of collisions between the particles and the container, so increases the total force exerted by all the collisions

State Kepler's Third Law See diagram on page 27

The period of the orbit and the mean distance between the Sun and the planet are related by Kepler's third law: T² ∝ r³

Define: Specific latent heat

The specific latent heat (L) of fusion or vaporisation is the quantity of thermal energy required to change the state of 1 kg of a substance

What is the only way Hadrons can decay?

Via the Weak Nuclear Force - it is the only thing that can change one type of quark into another.

(Useful Extra Equation) Give a formula relating moles, mass and molar mass (g/mol) (relative formula mass in grams)

n = M/Mr

(Equation) Give the equation relating pressure, number of particles, their mass and speed. Give all the various units

pV = 1/3Nmc² (c² should have a bar over it - see textbook) p = Pressure (Pa) V = Volume (m³) N = number of particles m = mass (kg) c(bar)² = mean square speed - it represents the mean of the squared speed of all the particles

(Equation) Give the formula for escape velocity and give the units

v = √(2GM/r) Units of ms⁻¹

Explain the different elements of the equation: v = √(GM/r) and give units for each

v is orbital speed in ms⁻¹ G is gravitational constant 6.67x10⁻¹¹ in Nm²kg⁻² M is the mass of the object being orbited (the larger one in the centre) (kg) r is the distance form the centre of the object being orbited to the centre of the orbiting satellite (m)

Give a formula relating work done, mass and gravitational potential

ΔW = mΔVg Where ΔW is the work done (J), m is the mass of the object (kg) and ΔV is the gravitational potential difference (Jkg⁻¹)